We present a mid-infrared (MIR) source based on intra-pulse difference-frequency generation under the random quasi-phase-matching condition. The scheme enables the use of non-birefringent materials whose crystal orientations are not perfectly and periodically poled, widening the choice of media for nonlinear frequency conversion. With a 2 μm driving source based on a Ho:YAG thin-disk laser, together with a polycrystalline ZnSe element, an octave-spanning MIR continuum (2.7-20 μm) was generated. At over 20 mW, the average power is comparable to regular phase-matching in birefringent crystals. A 1 μm laser system based on a Yb:YAG thin-disk laser was also tested as a driving source in this scheme. The new approach provides a simplified way for generating coherent MIR radiation with an ultrabroad bandwidth at reasonable efficiency.